Predicting dry matter production of cauli¯ower
(
Brassica oleracea
L.
botrytis
) under
unstressed conditions
Part II. Comparison of light use ef®ciency and
photosynthesis±respiration based modules
H. Kage
*, H. StuÈtzel, C. Alt
Institute for Vegetable and Fruit Crops, University of Hannover, Herrenhaeuser Strasse 2, D-30419 Hannover, Germany
Accepted 10 May 2000
Abstract
Six different modules for dry matter production of cauli¯ower were parameterised and evaluated using a database of 22 cauli¯ower crops originating from 15 independent ®eld experiments. The evaluation included a light use ef®ciency, LUE, based module assuming LUE to be constant, an LUE based module assuming a linear decrease of LUE with increasing daily photosynthetically active radiation sum, I, two photosynthesis±respiration based modules using an analytical integration of the rectangular hyperbola over the canopy, assuming either the light saturated photosynthesis rate of single leaves,Pmax, to be constant or to decrease proportionally to irradiance within the canopy. Furthermore two slightly modi®ed versions of the light interception and photosynthesis algorithms of the SUCROS model were evaluated, where the negative exponential equation for single leaf photosynthesis was replaced by the rectangular hyperbola. In order to make these modules comparable with the analytical integration approach,Pmaxwas also assumed to be either constant or to decrease proportionally to irradiance within the canopy.
The results indicate that an estimated constant LUE (3.15 (0.04) g MJÿ1) is only poorly able to predict total dry matter production for cauli¯ower (modelling ef®ciency EF0.69) of an independent data set. Using a linear decline of LUE withI (LUE6.66 (0.80)±0.36 (0.08)I) drastically increased the predictive value (EF0.88) of the LUE approach. The descriptive and predictive value of the photosynthesis based modules was higher when assuming thatPmaxdeclines within the canopy. Then the predictive value of the photosynthesis/respiration based approach was
*
Corresponding author. Tel.:49-511-762-2919; fax:49-511-762-3606.
E-mail address: [email protected] (H. Kage).
better than the simple LUE approach but not generally better than the LUE approach assuming a linear decrease of LUE with increasing daily radiation sum.# 2001 Elsevier Science B.V. All rights reserved.
Keywords: Cauli¯ower; Model; Dry matter production; Daily radiation sum
1. Introduction
The level of abstraction in modules for calculating crop dry matter production rate varies considerably, models relying on the concept of light use ef®ciency, LUE (Jones and Kiniry, 1986; Williams et al., 1989; Chapman et al., 1993) representing an approach at a higher abstraction level on the one hand and photosynthesis±respiration based modules (Spitters et al., 1989) representing a more detailed, bottom up approach on the other hand. The LUE concept has become a popular approach for calculating total dry matter production rates in crop growth models mainly due to its simplicity and to the experimental evidence that the ratio between the time integral of intercepted radiation and dry matter production seems to be quite constant (Monteith, 1977; Gallagher and Biscoe, 1978; Garcia et al., 1988). However, the validity of this concept has also been subject to exhaustive debate (Demetriades-Shah et al., 1992, 1994; Arkebauer et al., 1994; Monteith, 1994). Theoretical analyses (Hammer and Wright, 1994; Dewar, 1996; Haxeltine and Prentice, 1996; Dewar et al., 1998; Medlyn, 1998; Kage et al., 2001) have shown that a constant LUE over a wider range of daily photosynthetic active radiation sum is only likely as an effect of a combined adaptation of the photosynthetic apparatus to the radiation environment within the canopy and over time. It is, however, dif®cult to decide by up-scaling from single leaf to canopy photosynthesis and crop dry matter production rates alone whether LUE is strongly in¯uenced by daily radiation sum as long as the functional relationships between parameters like the light saturated photosynthesis rate,
Pmax, and environmental variables changing within the canopy and with time are
not known.
If such detailed knowledge is not available, one can make assumptions about the behaviour ofPmaxwithin the canopy, adjust the model to data measured at the
and Saeki (1953). However, more detailed approaches have been developed since then (de Wit, 1965; Goudriaan, 1977; Spitters, 1986; Spitters et al., 1986), separating diffuse and direct radiation components and considering the effects of latitude and season on the radiation geometry. We therefore included also modules calculating radiation interception of crop canopies at a different level of detail within our analysis.
Our objective was to evaluate the usefulness of different approaches for calculating total dry matter production within the crop growth models differing in their level of detail in process description. We used for this study data from 22 crops from 15 ®eld experiments with cauli¯ower grown for 4 years at one location in northern Germany.
2. Materials and methods
2.1. Field experiments
The ®eld experiments used in this study are mainly the same as previously described by Kage and StuÈtzel (1999b). Therefore, only a brief description will be given here. In addition to the data set described in Kage and StuÈtzel (1999b) data from two nitrogen fertilisation trials from 1996 to 1997 on the same experimental ®elds are included. From this experiments only the optimum and super optimum nitrogen supply rates 300 and 450 kg N/ha were used.
The whole set of ®eld experiments from four consecutive years were divided into two groups, one for derivation of the parameters of the model and a second, independent group for the evaluation of the model. Both groups of ®eld experiments were conducted on the same experimental farm located 15 km south of Hannover, Germany, on a typical loess derived hapludalf soil. Whereas in the parameterisation group of experiments two cultivars were used, i.e. `Fremont' and `Linday' in the second group only the cultivar `Fremont' was used. Crops were established in the ®eld using transplants grown in peat cubes of 4 cm edge length, the average visible leaf number at planting ranged from 2.9 to 4.03 leaves per plant. Crop husbandry in all experiments was regarded to ensure a crop growth not limited by the supply of nitrogen or water. Pesticides were applied when needed to ensure a healthy growth.
2.2. Modules
The modules used in this study for calculating development and partitioning are essentially the same as those described in Kage and StuÈtzel (1999b). The development module distinguishes a juvenile, a vernalization and a generative phase in the development of cauli¯ower (Wiebe, 1972a,b,c). The dry matter partitioning part includes an allometric approach to dry matter partitioning between leaf and stem and an empirical logistic function describing the fraction of dry matter allocated to the curd depending on the temperature sum after the end of the vernalisation process. However, a slight re-parametrisation of the partitioning module was carried out in order to obtain the best possible description of development and partitioning. For this purpose the group of experiments was used from which also the parameters of the dry matter production modules were estimated.
For dry matter production six different modules were calibrated and evaluated against the data set. We used two modules based on the light use ef®ciency approach and four based on a photosynthesis±respiration approach (Table 1).
The amount of absorbed photosynthetically active radiation (PAR),Q(MJ mÿ2 per day) is calculated from the daily sum of photosynthetically active radiation recorded above the canopy, I (MJ mÿ2 per day) and the leaf area index, LAI (Monsi and Saeki, 1953):
QI 1ÿeÿkLAI (1)
wherek is the extinction coef®cient forI (ÿ), taken as 0.65. The growth rate of shoot dry matter of the crop (g DM mÿ2 per day) may be calculated as the product of Q, LUE and a temperature correction factor fTemp(ÿ):
dW
dt QLUEfTemp (2)
The value of fTemp is 1 within a range from 10 to 258C average daily air
temperature and is linearly decreasing to 0 from 10 down to 08C and from 25 to 358C. The model module LUE I assumes LUE to be constant, therefore being a parameter within the model. In this study we examined, however, also the hypothesis that LUE is a function of I. This function may be approximated as being linear for a particular range ofI:
LUELUE0ÿaLUEI (3)
LUE then is a variable dependent on the two parameters LUE0 (g MJÿ1),aLUE
(g DM MJÿ2m2 per day) and the level ofI.
Differently from the model presented in Kage and StuÈtzel (1999b), the speci®c leaf area, SLA (cm2gÿ1) of newly formed leaf area is now calculated as a function of the average PAR during the last 10 daysIavusing the function of Alt
(1999):
SLA590Iavÿ0:851 (4)
Table 1
Abbreviations and short description of the modules for total dry matter production used in this study
Module name Short description
LUE I Constant LUE, radiation absorption according to Monsi and Saeki
LUE II As LUE I, but LUE assumed to be a linear function of average daily radiation sum ACOCK I Analytical integration of the rectangular hyperbola for single leaf photosynthesis over the canopy, numerical 3-point gauss integration over time, respiration according to SUCROS assumptions
ACOCK II As ACOCK I, but assumption of a decline ofPmaxwithin the canopy proportional to irradiance
SUCROS I Original algorithms from SUCROS, separating direct and diffuse radiation, but negative exponential function for single leaf photosynthesis replaced by rectangular hyperbola
The LAI of the crop then is calculated from
dLAI dt
dWL
dt SLA (5)
The SLA of the analysed cauli¯ower crops at transplanting was not always measured but with an average value of about 200 cm2gÿ1was consistently higher than predicted from Eq. (4) which was derived from measurements at later growth stages. LAI was therefore initialised using measured leaf dry matter at transplanting and a value for SLA of 200.
It has to be noticed that we neglected root growth at this stage of the analysis; our estimates for LUE are, therefore, also only valid for calculations of aboveground dry matter production.
The two photosynthesis based modules, ACOCK I and ACOCK II, have been described in Kage et al. (2001). Also the respiration part of these modules, which is essentially based on the assumptions used in the SUCROS model (Goudriaan and van Laar, 1994) is described there.
In order to evaluate the effect of differentiation between shaded and unshaded leaf classes within the canopy and of a more detailed approach of radiation interception on the descriptive and predictive capability, we included also the algorithms from the procedures ASTRO, ASSIM and TOTASS of the SUCROS model (Goudriaan and van Laar, 1994) to calculate total daily assimilate production in our evaluation. In order to make this module comparable with our ACOCK based submodules we replaced the negative exponential function used in ASSIM to calculate photosynthesis rate per unit leaf area with the rectangular hyperbola. This module is further referred as SUCROS I (Table 1). The parameter initial light use ef®ciency,a, of the rectangular hyperbola was set to a value of
25mg Jÿ1 as indicated by the measurements of Kage et al. (2001).
In order to facilitate a comparison between the SUCROS module and the ACOCK II module, we also included the option to let the light saturated photosynthesis rate Pmax decrease within the canopy according to the pro®le of
diffuse radiation
PmaxPmax0eÿkdifLAI (6)
where Pmax0 is the light saturated photosynthesis rate of unshaded leaves at the
top of the canopy andkdifis the extinction coef®cient for diffuse radiation which
is calculated according to Spitters et al. (1989). This version of the SUCROS based module is further called SUCROS II (Table 1).
Radiation absorption Rabs within the canopy is calculated according to the
whereDLis the day length,WDL andwLAI are weighting coef®cients:
We had serious dif®culties to simulate the dry matter production of the experiments from the evaluation group with early planting dates (day 97 in 1994, 94 in 1995 and 100 in 1996), the measured total dry matter being substantially and consistently smaller than the simulated total dry matter. We interpreted this as re¯ecting problems in plant establishment which were probably caused by frost and low temperatures. Since we are not yet able to include these effects into the model, we started our simulations for these data sets not from planting but from the ®rst measurement of plant dry matter, which was usually about 4 weeks after planting.
2.3. Parameter estimation and statistics
The whole model is implemented within the HUME modelling environment (Kage and StuÈtzel, 1999a). This modelling environment supports parameter estimation based on the Marquardt algorithm (Marquardt, 1963) and allows easily sub-model exchange because of its modular object oriented structure. We used the unweighted square sum of differences between simulated and measured total dry matter as the objective function for estimating LUE, LUE0,aLUE,PmaxandPmax0.
For a re-parametrisation of some of the parameters of the development and dry matter partitioning modules unweighted square sums of the differences between simulated and measured model variables were used. For the parametersk1,k2leaf
numbers for g, h stem dry matter and for rf curd dry matter was used as the
objective variable. The whole parameter estimation procedure including the estimation of the parameters of the dry matter production modules was repeated 3±4 times until no further signi®cant change in any parameter value could be detected. The new parameter values are shown in Appendix A.
The descriptive and predictive power of a model can be evaluated by linear regression of the output and measured data and several other statistical measures. One of them is the modelling ef®ciency, EF (Smith et al., 1997):
EF1ÿ
Akaike information criterion, AIC (Akaike, 1969).
where n is the number of observations and p is the number of parameters. The descriptive and predictive power of models is higher the lower the value of the AIC. Another statistical parameter used in this study is the root mean square error, RMSE:
giving the average model prediction error.
3. Results
The two sets of ®eld experiments used in this study differed with respect to the variability of mean daily radiation sum during the growing period of each crop (Table 2). Whereas in the ®rst set that was mainly used for calibration, only a small variation, ranging from 8.35 to 9.29 MJ mÿ2per day could be observed, in the second set of experiments, that was mainly used for evaluation, a considerable range ofIvalues from 5.45 to 8.13 MJ mÿ2per day was measured. The reason for this higher variability is the late planting date of some crops of this group (Fig. 1). The variability in mean air temperature is generally smaller than the variability in daily radiation sum, since temperature declines not as much in autumn as daily radiation sum does (Fig. 1).
As a ®rst step in our analysis we estimated the parameters LUE of module LUE I as well as the Pmax and Pmax0 values of the modules ACOCK I and II
and their asymptotic standard errors, respectively, for every experiment separately and plotted them against the mean daily radiation sum during the crop's growth period (Fig. 2). Fitting the two parameter module LUE II was avoided during this step because of the limited number of observations in every experiment.
Linear regression analysis showed no signi®cant correlation between LUE and mean photosynthetically active daily radiation sum for the calibration data set, nor for the evaluation data set alone. However, using the parameter estimates from both sets of experiments a signi®cant correlation could be found (Fig. 2a). No correlation exists for the parametersPmaxandPmax0and mean daily radiation
sum during the growing periods of the different crops (Fig. 2b).
production modules. Calibrating the module LUE I with the data of the calibration set gave a mean value for LUE of 3.15 (g DM MJÿ1) (Table 3). The parameter estimation for module LUE II, however, indicates a signi®cant in¯uence of the mean daily radiation sum on LUE, since we found a parameter value foraLUEsigni®cant different from zero (Table 3). The values foraLUEand
LUE0 we obtained are higher than slope and intercept of the linear regression
between mean daily radiation sum during the growing period and LUE values estimated for a particular crop (Fig. 2b).
Estimating the values of Pmax and Pmax0 for the calibration data set gave
signi®cantly different values for both parameters either using the ACOCK or the SUCROS approach (Table 3). This is not an unusual result since an assumed decline of Pmax within the canopy as in Acock II and SUCROS II has to be
compensated by a higher Pmax at the top of the canopy in order to predict the
same dry matter production rate.
Table 2
Year, data group, planting and harvest dates, average daily sum of photosynthetically active radiation and average temperature during the growth period of the cauli¯ower experiments used in this study
1994 Calibration Fremont 124 194 8.72 15.12
1994 Fremont 152 236 9.24 18.31
1994 Linday 124 194 8.72 15.12
1994 Linday 152 247 8.80 18.03
1995 Fremont 122 200 8.35 14.76
1995 Fremont 137 207 8.48 16.00
1995 Fremont 164 234 9.29 18.79
1995 Linday 122 204 8.41 15.13
1995 Linday 137 209 8.49 16.12
1995 Linday 164 253 8.41 18.02
1994 Evaluation Fremont 97 185 8.13 13.12
1994 Fremont 207 293 5.45 14.52
1995 Fremont 94 187 7.59 12.13
1995 Fremont 200 291 6.10 16.49
1995 Fremont 207 298 5.56 15.69
1996 Fremont 100 189 7.41 12.59
1996 Fremont 200 284 6.18 14.34
1996 Fremont 206 305 5.11 13.45
1996a Fremont 170 240 7.78 16.08
1997a Fremont 190 258 7.23 18.56
a
We also used the second data set which will later be used to evaluate the predictive value of our model for proving the constancy of parameter values. The values obtained from this database are slightly but not signi®cantly different from the formerly estimated values for the module LUE II. For all photosynthesis based modules somewhat lower values forPmaxwere estimated for the evaluation
data set. For the LUE I module a signi®cant higher value of LUE was obtained (Table 3).
The descriptive and predictive value of the modules was evaluated by comparison of simulated with measured total dry matter production data from the parameterisation and evaluation data sets using, for both data sets, the parameter values obtained from the calibration data set. Both versions of the LUE based dry matter production module seem to have similar descriptive power for the calibration data set (Table 4 and Fig. 3a). The linear regressions between simulated and measured total dry matter values have in both cases a slope and an intercept not signi®cantly different from 1 and 0, respectively, and comparable modelling ef®ciencies 0.92 for the LUE I and 0.94 for the LUE II module. The
situation is, however, somewhat different for the application of the LUE based modules on the evaluation group of experiments. (Table 4 and Fig. 3). The LUE II module was able to give also for the evaluation data an acceptable prediction (EF0.88), compared to the LUE I module (EF0.69).
Looking at the descriptive and predictive value of the photosynthesis modules (Table 4 and Fig. 3), we see that the ACOCK II module has a descriptive value close to the LUE II module, whereas the ACOCK I module has a low, but still acceptable descriptive value for our calibration data set. It is, however, much less able to predict the dry matter production of our evaluation data set (Table 4 and Fig. 3). The descriptive value of the SUCROS modules is not superior to the ACOCK modules, but especially the SUCROS II module seems to have a relatively high predictive value (Table 4).
The data points of the photosynthesis/respiration modules tend to lie above the 1/1 line if one assumes a constantPmaxand they lie mostly below the 1/1 line for
the assumption of a decreasingPmaxwithin the canopy (Fig. 3). This is due to the
fact that the predicted time course of dry matter production differs in the way that, in general, the modules which assume a constant Pmax within the canopy
estimate a lower production during the early crop growth phase which is over-compensated during the later growing phase (Fig. 4). The LUE modules predict an almost constant dry matter increase under conditions of quite stable values of daily radiation sum. For a late planted crop, however, which is growing
Table 3
Parameter estimations for four dry matter production modules assuming either a constant LUE or an LUE being a linear function of daily average radiation sum,I(MJ mÿ2per day) (LUELUE0± aLUEI) for two different photosynthesis/respiration based modules for two groups of experimentsa
Data set Module Parameter Value S.E.
Calibration LUE I LUE 3.15 0.04
LUE II LUE0 6.66 0.80
Evaluation LUE I LUE 3.49 0.08
LUE II LUE0 6.74 0.51
Table 4
Number of ®tted parametersp, coef®cient of determination for the model predictionr2, AIC and parameters of the linear regression between simulated and measured total above ground dry matter of cauli¯ower crops from calibration and evaluation groups of experiments using four different dry matter production modulesa(for explanation of modules, see Table 1)
Data set Module p EF RMSE AIC Slope Intercept r2 n
Calibration LUE II 2 0.941 98.706 555.1 0.98 (0.03) 27.99 (17.20) 0.94 60
ACOCK II 1 0.916 118.185 574.7 1.04 (0.04) ÿ35.78 (22.56) 0.92 60
LUE I 1 0.916 114.381 574.7 0.95 (0.04) 23.22 (20.26) 0.92 60
SUCROS I 1 0.901 127.918 584.2 0.98 (0.04) 1.83 (23.81) 0.90 60
ACOCK I 1 0.886 137.684 593.0 0.89 (0.04) 47.80 (22.81) 0.90 60
SUCROS II 1 0.882 139.944 594.9 1.10 (0.05) ÿ59.63 (27.26) 0.89 60
Evaluation LUE II 2 0.879 113.914 411.2 0.88 (0.05) 39.39 (25.16) 0.90 43
ACOCK II 1 0.833 134.040 423.2 0.86 (0.05) 11.56 (28.78) 0.88 43
SUCROS II 1 0.820 139.003 426.4 0.93 (0.07) 5.19 (35.08) 0.83 43
SUCROS I 1 0.780 153.566 434.9 0.82 (0.06) 70.87 (32.42) 0.82 43
LUE I 1 0.690 182.547 449.8 1.07 (0.11) 108.79 (42.15) 0.78 43
ACOCK I 1 0.682 184.784 450.9 0.70 (0.05) 93.54 (28.53) 0.85 43
a
Modules are grouped by data set and AIC.
H.
Kage
et
al.
/Scientia
Horticultur
ae
87
(2001)
under a decreasing daily radiation sum, the LUE II module is clearly superior to all other modules, as it compensates lower daily radiation sum by an increasing LUE.
Plotting the calculated daily light use ef®ciencies of the ACOCK I and II modules for an early and a late planted cauli¯ower versus the daily radiation sum values, a considerable scatter of calculated LUE on a daily basis becomes obvious. This is because variations in temperature and crop dry weight at similar levels of daily radiation sum affect respiration losses and thereby net assimilation values. However, there is also a clear decrease of LUE with increasing daily radiation sum values (Fig. 5). This trend corresponds well with the functional relationship between LUE andI estimated for the LUE II module (Fig. 5).
Fig. 4. Measured and simulated shoot dry matter of cauli¯ower crops cv. `Freemont' planted early (a) (DOY 122) and late (b) (DOY 164) in 1995 vs. time using six different modules for calculating dry matter production (for explanation of modules, see Table 1).
Fig. 5. Light use ef®ciency as a function of daily sum of photosynthetically active radiation simulated with two different optimised photosynthesis modules assuming either a constantPmax
4. Discussion
The aim of this paper is to evaluate different modules for predicting dry matter production of cauli¯ower under unstressed conditions, i.e. in the absence of water and nutrient limitations and pest damages. The database we used for this purpose is quite large concerning the number of independent experiments included, but limited with respect to the kind of data we included in the analysis as we used only time series data of total dry matter and the environmental data of temperature and radiation.
Our analysis shows that LUE for unstressed cauli¯ower crops is not constant, but decreases with increasing daily radiation sum (Fig. 2, Table 3). The observed decrease of LUE withIagrees with measurements of Olesen and Grevsen (1997) and calculations of Medlyn (1998). From data of the ®rst mentioned authors we estimated a linear decrease of LUE±I of LUE6.3±0.34I, whereas for Medlyn's (1998) data we estimated a decrease of 0.33 g DM MJÿ2mÿ2 per day. From theoretical considerations (Kage et al., 2001), however, it seems to be likely that LUE is a non-linear function ofIand that the slope of the LUE±Ifunction is also less negative for higher LAI values. A linear approximation, like the one we present, may therefore be valid only for a limited range of daily radiation sum and may be further re®ned by including an in¯uence of LAI.
The estimated values ofPmaxandPmax0for our photosynthesis based modules
(Table 3) are within the range of the measured values presented in Kage et al. (2001), maybe despite the value for the SUCROS II module. But the assumption that Pmax values decline directly proportional to the irradiance level within the
canopy probably overestimates the degree of light adaptation within the canopy (Kage et al., 2001). Too high estimates forPmax0 values are therefore needed to
compensate this error.
Kage et al. (2001) showed that whether one assumes a decline ofPmax within
the canopy or not, LUE seems to be a negative function of PAR. Therefore, the different predictive value of the ACOCK I and II and the SUCROS I and II modules for dry matter production (Table 4) cannot mainly be explained by a different change of LUE under varying daily radiation sum values. The difference in the predictive value of the modules seems to be mainly caused by the fact that for a constant Pmax within the canopy (ACOCK I, SUCROS I) LUE increases
with increasing LAI whereas it decreases for aPmaxdecreasing proportionally to
irradiance level within the canopy (ACOCK II, SUCROS II). Consequently, different time courses of dry matter production are predicted (Fig. 5). This increase of LUE with increasing LAI, which is largest for the ACOCK I module, probably is the reason for its inferior descriptive and predictive power (Table 4). This may also hold as an argument that the assumption of the ACOCK II and SUCROS II modules, a decline of Pmax within the canopy, is somewhat more
other hand may be regarded as an indication that the adaptation of Pmax to a
changing radiation environment over time is limited, since the analysis presented in Kage et al. (2001) shows that this process seems to be a prerequisite for a constant LUE.
The more detailed light interception approach of the SUCROS modules did not improve the descriptive and predictive value compared to the simple Monsi±Saeki approach. Our data set indicates that different assumptions about the behaviour of
Pmax within the canopy, seems to be more important than the consideration of
direct and diffuse radiation in light interception calculations. But it has to be noticed that we did not include in our module comparison any approach which explicitly accounts for the inhomogeneous leaf area distribution of cauli¯ower during the ®rst weeks after transplanting. Thereby, we may probably have overestimated light interception during the early growth phase. However, also the leaf angle distribution of cauli¯ower changes according to our observations to some extent from a quite planophile to a more spherical one. This may lead to a decreasingkvalue over time which may compensate for some of the effects of an uneven leaf distribution. Also the SLA of cauli¯ower at early growth stages is higher than calculated from Eq. (4) (data not shown), which leads to a more rapidly canopy closure and therefore also compensates for some of the structural errors of our light interception model. At least in the second half of their growth period, however, the crops we analysed had high values of LAI and a quite homogenous leaf area distribution (data not shown).
One reason for the popularity of the constant LUE concept seems to be the possibility to derive this parameter directly from measurements in ®eld experiments by plotting total dry matter data of a crop vs. values of cumulative intercepted radiation and to interpret the slope of the linear regression as LUE. This method has the shortcoming that one usually has to assume a constant LUE throughout the growing season or at least over a longer time period in order to get a suf®cient amount of data pairs. Variations of LUE due to rapidly changing environmental conditions like radiation and temperature can therefore not easily be detected. Even if one is able to identify such a relationship (Fig. 2) this is only valid at the timescale at which it was evaluated. This becomes clear from the distinct effects of daily radiation sum on LUE at the timescale of a cropping period and on a daily basis (cv. Fig. 2 and Table 3).
dynamic models. But also LUE based approaches may be further re®ned by parameter estimation techniques and an appropriate database. The approach we used for calibration of our LUE II module, for instance, resulted in a simple structured module with good descriptive and predictive value. Adjusting parameters of dynamic crop growth models like LUE or Pmax by minimising
the prediction error for an aggregated variable like total above ground dry matter on the other hand implies the risk, that structural errors of a model are masked and the estimated parameter values are biased. This cannot totally be ruled out for our analysis, but since the obtained parameter values are well within a physiological meaningful range, we do not expect that these effects are serious. Recognising that Pmax seems to be a more conservative parameter than LUE
(Fig. 2) one may conclude that even if based on several assumptions, the parameterisation of a photosynthesis±respiration based approach usually gives more generally applicable predictions than an LUE based approach. However, the usefulness of the constant LUE concept for calculating dry matter production in crop growth models cannot be judged ultimately from the presented analysis. At least for annual crops which have a limited time span for sowing or planting each year, it seems likely that year to year variation in average daily radiation sum during cropping time at one location is small (see analysis of Medlyn, 1998). For a particular crop grown under these conditions constant LUE values may allow suf®cient exact predictions of crop productivity.
The failure of the constant LUE concept in predicting total dry matter production can be regarded as an indication that the requirements for a constant LUE which were deduced from theoretical analyses are not ful®lled for cauli¯ower. Possible reasons for this may be seen in the quite short growing season and the high growth rate of this crop, which limits the time available for adaptation processes. The fact that we were able to detect the limited constancy of LUE for cauli¯ower with experiments at one location only is probably due to the short growing period of this crop, which makes it possible to cultivate this crop under substantially different radiation regimes.
5. Conclusions
and is therefore of superior descriptive and predictive value compared to simple LUE models. Our results indicate that assumptions about the behaviour ofPmax
within the canopy seem to be of higher importance for correct predictions than detailed calculations of light interception.
Acknowledgements
The authors debt credit to M. Kling and E. Diedrich for careful ®eld work. The helpful comments of the editor and two unknown reviewers are gratefully acknowledged.
Appendix A.
The following table shows the name and values of parameters from the development and partitioning model (Kage and StuÈtzel, 1999b) as well as the equation number from the original publication. Parameters set with an * are changed in this study.
Name Value Equation No.
k1* (leaf per leaf8Cÿ1 per day) 0.00392 (1)
k2* (leaf8Cÿ 1
per day) 0.0424 (3)
g* 1.617 (18)
h* ÿ4.958 (18)
f0 0.000215 (21)
rf* (8Cÿ1 per day) 0.0133 (21)
ff 0.815 (21)
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